Well...I haven't actually got Warband yet...but I imagine I would start similarly to how I did in vanilla. There are actually two approaches, depending on whether you want to play a "good" or "bad" character.
For a "good" character, you start off with a small party (ie., yourself) and trade. A lot. One of your first "purchases" should be one of the trade-skill heroes (if you haven't given yourself trade skill), along with one of the "scout" heroes (path-finding, tracking, etc.). When they start levelling up, make sure to give them at least a point or two of riding, and the necessary agility, so they can ride a horse and let your party move much faster on the world map. Keep trading, and kit yourself and your team out (continuing to hire heroes until you have a full party--that's 9, at least in vanilla, since there are two sets of 8 which mutually dislike each other). Once you've done that (and it will probably take a few tens of thousands of denars for decent equipment), start fighting bandits--not the huge parties, but ones not more than 12-15 people. It's better to start with smaller bands of looters and what not (which usually, but not always, spawn near the training grounds), and remember that you can easily level up once or twice going through the training grounds and then sparring with your companions (which can help them level up, too). Fight in tournaments from time to time, but don't spend a lot on bets in case you get screwed (get weapons you're not skilled with) or just plain lose, since you don't have a high skill level and toughness yet. Once your renown is up fairly high, start hiring soldiers to assist you. Recruits are recommended. Having at least one trainer character by this point is highly recommended, as is giving yourself trainer regardless. This will make levelling them up go much more quickly. Start taking quests, but don't be too afraid to refuse/abandon ones that are beyond your ability to complete. At this point, with around 20-40 soldiers, you should think about pledging yourself to a king, and you should really start hunting down bandits wherever you see them. Beyond that I cannot go (haven't gotten there yet!)
For an evil character, it's much more straightforward, with less trading. First, you should focus on trading and doing some quests (the Fed-Ex ones) for kitting yourself out and getting the other heroes. Then, try to fight in some tournaments or kill some bandits to get some renown, enough to be hired as a mercenary leader by one of the factions. When that happens, build a little army and start raiding enemy villages. Helps if you're Khergits or have good on-map speed (but your small party should be able to outrun most lords). This is really profitable. Use all the money to kit out all your men and yourself in the best gear you can find, improve your fiefs (once you get enough renown to establish yourself) and so on. Keep improving your renown. Again, I haven't gone beyond this point.